We revisit the 1/2-BPS D-branes in the AdS$_5\times$S$^5$ background. Based only on the classification of 1/2-BPS D-branes obtained by the covariant open string description, we consider various purely static configurations or embeddings of D-branes without any worldvolume fluxes in the AdS$_5\times$S$^5$ background. Under the covariant $\kappa$ symmetry fixing condition, we investigate the supersymmetries realized on the D-brane worldvolumes and obtain the worldvolume supersymmetry transformation rules to leading order in the worldvolume fields. We show that only the AdS type D-branes, in which the AdS radial direction is a worldvolume coordinate, are 1/2-BPS.